Simplify the following expression: $r = \dfrac{q^2 - 11q + 30}{q - 5} $
Explanation: First factor the polynomial in the numerator. $ q^2 - 11q + 30 = (q - 5)(q - 6) $ So we can rewrite the expression as: $r = \dfrac{(q - 5)(q - 6)}{q - 5} $ We can divide the numerator and denominator by $(q - 5)$ on condition that $q \neq 5$ Therefore $r = q - 6; q \neq 5$